Data Multi-Fiber Tractography Visualizations for Diffusion MRI€¦ · Multi-Fiber Tractography Visualizations for Diffusion MRI Data Sjoerd B. Vos*, Max A. Viergever, Alexander Leemans

Multi-Fiber Tractography Visualizations for Diffusion MRIDataSjoerd B. Vos*, Max A. Viergever, Alexander Leemans

Image Sciences Institute, University Medical Center Utrecht, Utrecht, The Netherlands

Abstract

In recent years, several new diffusion MRI approaches have been proposed to explore microstructural properties ofthe white matter, such as Q-ball imaging and spherical deconvolution-based techniques to estimate the orientationdistribution function. These methods can describe the estimated diffusion profile with a higher accuracy than themore conventional second-rank diffusion tensor imaging technique. Despite many important advances, there are stillinconsistent findings between different models that investigate the “crossing fibers” issue. Due to the high informationcontent and the complex nature of the data, it becomes virtually impossible to interpret and compare results in aconsistent manner. In this work, we present novel fiber tractography visualization approaches that provide a morecomplete picture of the microstructural architecture of fiber pathways: multi-fiber hyperstreamlines andstreamribbons. By visualizing, for instance, the estimated fiber orientation distribution along the reconstructed tract ina continuous way, information of the local fiber architecture is combined with the global anatomical informationderived from tractography. Facilitating the interpretation of diffusion MRI data, this approach can be useful forcomparing different diffusion reconstruction techniques and may improve our understanding of the intricate whitematter network.

Citation: Vos SB, Viergever MA, Leemans A (2013) Multi-Fiber Tractography Visualizations for Diffusion MRI Data. PLoS ONE 8(11): e81453. doi:10.1371/journal.pone.0081453

Editor: Gaolang Gong, Beijing Normal University, China

Received August 20, 2013; Accepted October 13, 2013; Published November 25, 2013

Copyright: © 2013 Vos et al. This is an open-access article distributed under the terms of the Creative Commons Attribution License, which permitsunrestricted use, distribution, and reproduction in any medium, provided the original author and source are credited.

Funding: This work was financially supported by the project Care4Me (Cooperative Advanced REsearch for Medical Efficiency) in the framework of the EUresearch program Information Technology for European Advancement. The funders had no role in study design, data collection and analysis, decision topublish, or preparation of the manuscript.

Competing interests: The authors have declared that no competing interests exist.

* E-mail: [email protected]

Introduction

Diffusion MRI can be used to estimate the self-diffusion ofwater molecules in vivo (e.g., Moseley et al. [1]). Diffusiontensor imaging (DTI) describes the orientational preference ofdiffusion in the human brain, modeling it as a second-ranktensor [2]. Based on the diffusion tensor framework, virtualreconstructions of white matter (WM) fiber pathways can becreated with fiber tractography (e.g., Basser et al. [3]). Toconvey more information than merely the fiber trajectories,alternative approaches to the conventional streamlines and -tubes have been proposed: hyperstreamlines, showing thesecond and third eigenvectors and eigenvalues of the diffusiontensor as the cross-sectional shape of the streamtube [4]; andstreamribbons, where the local width of the ribbon indicates thecoefficient of planar diffusion [5,6]. However, the additionalinformation visualized in this way suffers from the samelimitations inherent to DTI, i.e., the inability of the diffusiontensor to describe the diffusion correctly in regions of crossingor branching fiber tracts [7-12].

To overcome the limitations of DTI, several different methodshave been proposed, e.g., Q-ball imaging (QBI) [13],constrained spherical deconvolution (CSD) [14], diffusionspectrum imaging (DSI) [15] – each having differentrequirements in terms of the acquisition protocol. QBI and DSI,on the one hand, have a direct mathematical relation betweenthe measured diffusion signals and the estimated diffusionorientation distribution function (ODF) and diffusion propagator,respectively. The propagator obtained from DSI represents the3D probability of spin displacement, where the diffusion ODF(dODF) calculated by QBI yields only the orientational aspectof the spin displacement [16]. On the other hand, CSD uses anestimated single fiber response function to deconvolve the DWintensities with this response function to obtain the fiber ODF(fODF), specifying the orientations of the underlying fiberpopulations. Tractography that makes use of these ODFs,which then is referred to as “multi-fiber” tractography, can takecrossing fibers configurations into account, such as, forinstance, in the centrum semiovale, where the cortico-spinaltracts (CST), arcuate fasciculus (AF), and lateral projections of

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the corpus callosum (defined in the remainder of this work as“latCC”) intersect one another [17-21].

With a growing number of diffusion MRI researchers optingfor these more advanced diffusion MRI methods overconventional DTI, especially for tractography purposes, it isbecoming increasingly important to fully utilize the potentialoffered by these approaches [22]. Despite the huge effortsinvested in creating these new techniques, there are stillseveral discrepancies and inconsistent findings betweendifferent algorithms (e.g., Jeurissen et al. [23]). To optimize theyield from diffusion data, it is important to understand theorigins of these differences. In this context, data visualizationplays an important role in facilitating the interpretation of high-dimensional diffusion MRI data. Visualization of the ODF isalready possible on a local scale as voxel-wise glyphrepresentations, which can be of great use to visualize theregional architectural complexity in known areas of crossingfibers [24]. However, as these local representations are onlyavailable for display at discrete positions [25-27], they aresuboptimal to convey the anatomical continuity of fiber bundles.To date, and to the best of our knowledge, there are no fibertractography visualization strategies that are specificallydesigned to address the interwoven and complex geometry ofthe WM fiber network [21,28,29].

In this work, we introduce an approach to visualize the localtissue architecture along reconstructed fiber tracts in acontinuous way, creating hyperstreamlines for multi-fibertractography data. This means that microstructural informationfrom advanced diffusion methods is combined with large-scaleanatomical information obtained from fiber tractography. Withthis new visualization method, the ODF is visualized along thefiber tracts to clearly illustrate the regions of crossing fibers.Additionally, by reducing the ODFs to their principal fiberorientations, streamribbons can be constructed to emphasizethe orientations of the crossing fiber populations. The proposedvisualization approaches create more complete representationsof the microstructural architecture in fibers that pass throughregions of complex WM configurations. As a result, these multi-fiber tractography visualizations may aid in our understandingof white matter organization. For clinical applications, improvedvisualization of local tissue microstructure along fiber tractsmay benefit surgical planning (e.g., 30,31). For neuroscientificpurposes, these visualizations could be used to compare

results between multiple diffusion MRI methods, aiding in theunderstanding of their behavior in complex fiber architecture(e.g., 23).

Materials and Methods

Ethics statementsAll subjects gave written informed consent to participate in

this study under a protocol approved by the University MedicalCenter Utrecht ethics board.

Tensor-Based VisualizationsBefore describing the multi-fiber visualization methods in

detail, we will first discuss why current DTI based tractvisualization approaches [4,6] are inappropriate for visualizingmulti-fiber tractography data. Consider two fiber populationscrossing at a 60° angle (Figure 1a,b). When these twopopulations coexist within one voxel – assuming slowexchange between these populations [7] – the resultingdiffusion tensor can be estimated from the averaged diffusionweighted signals of the individual populations (as shown inFigure 1c). The first eigenvector of this tensor (ε1, brown line inFigure 1c) will be an average of the two fiber populations (whitelines in Figure 1c). In DTI based tractography, the tractorientation will be determined by ε1, with ε2 and ε3 alwaysperpendicular to ε1 (Figure 1d). In the case of crossing fibers, ε1

is not necessarily parallel to one of the fiber populations asdetermined by the multi-fiber diffusion method (Figure 1c).Consequently, ε2 and ε3 will not necessarily be perpendicular tothe tract orientation for any of the two fiber populations, whichmeans that the information visualized in this way will bemisleading. The following will first detail the simulated fiberphantoms and in vivo data that will be used to demonstrate theconcepts and benefits of our multi-fiber tractographyvisualizations.

SimulationsTo illustrate the concepts of the multi-fiber visualizations and

to demonstrate the benefits over conventional tensor-basedvisualizations, we have created a toy example, where aconfiguration of three crossing neural fiber bundles has beensimulated. It is designed in such a way that one bundle has a

Figure 1. Conceptual difficulties of tensor-based visualizations of multi-fiber tractography data. In a) and b), two single fiberpopulations with their respective diffusion ellipsoids are shown. When these two coexist within one voxel (c), the first eigenvector (ε1

brown line) no longer corresponds to any of the underlying fiber orientations (white lines). d) The second (ε2 green) and third (ε3

blue) eigenvectors do not have a physical meaning with respect to the underlying fiber populations.doi: 10.1371/journal.pone.0081453.g001

Multi-Fiber Tractography Visualizations


smaller cross-section, so that there are regions with both twoand three fiber bundles intersecting each other, all crossingorthogonally (Figure 2a,b). To demonstrate the differencebetween the multi-fiber hyperstreamlines and streamribbons,another simulated phantom was designed in which not allpopulations cross at 90° angles (Figure 3a). Three fiberbundles were simulated, with two fiber populations crossingorthogonally (oriented inferior-superior and left-right) and onepopulation oriented largely along the anterior-posterior axis.Defined in a spherical coordinate system, the orientations are:1) inferior-superior, with azimuth angle θ=0° and polar angleφ=90°; 2) left-right, at θ=90° and φ=0°; and 3) mainly anterior-posterior, at θ=27° and φ=0°. Both phantoms were generated

with the following parameters: 60 gradient directions, a b-valueof 2500 s/mm2, and each single fiber population having afractional anisotropy and mean diffusivity of 0.7 and 0.7×10-3

mm2/s, respectively [32]. For regions with multiple fiberpopulations, we assume that there is only slow exchangebetween these populations [7].

In vivo diffusion MRI dataDiffusion MRI datasets were acquired from two healthy

subjects (a 25 year old female and a 25 year old male) on aPhilips 3T Achieva MR system (Philips Healthcare, Best, theNetherlands) using a single-shot spin echo EPI sequence, withone b=0 image and 60 diffusion-sensitizing directions acquired

Figure 2. Hyperstreamlines and streamribbons in a simulated crossing fiber phantom. The global topology of a simulatedfiber phantom is illustrated in a), with streamtubes color-encoded by the tract direction. The configuration was designed to containdistinct regions where two and three fiber populations intersect. fODF glyphs in this region clearly show these crossing populations(b). A single tract from the blue fiber bundle is shown in c) as tensor-based hyperstreamline and in d) as tensor-based streamribbon.In e), local fODF glyphs are shown along its trajectory, and a step-by-step creation of the hyperstreamline that envelops theseglyphs. In f), the cylindrical glyph objects represent the distinct fODF peaks and the streamribbon is a continuous visualization ofthese peaks.doi: 10.1371/journal.pone.0081453.g002



at a b-value of 2500 s/mm2 [33], using a SENSE accelerationfactor of 2. The acquisition matrix of 112×112 was zero-filled to128×128 with a field-of-view of 224×224 mm2, and 70contiguous axial slices with thickness 2.0 mm were acquired.Sequence timings were TE = 107 ms, TR = 10.3 s and theaverage SNR for both datasets was 20 (estimated from regionsin the centrum semiovale) [34].

Prior to data analysis, the datasets were corrected for eddycurrent induced geometric distortions and subject motion byrealigning all diffusion-weighted images to the b=0 image usingelastix [35], with an affine transformation model and mutualinformation as the cost function [36]. In this procedure, thediffusion gradients were adjusted with the proper b-matrixrotation [37].

Diffusion modeling and tractographyExamples of the proposed visualizations will be shown for

two diffusion reconstruction methods: CSD [14] and QBI [13].CSD estimates a response function of a single fiber population,assumes that all individual fiber populations are characterizedby this function, and then deconvolves the acquired signalintensities to resolve the fODF (further details can be found in

Tournier et al. [14]). In the QBI method employed, the acquireddiffusion weighted signal is modeled using sphericalharmonics, followed by the approximation of the dODF usingthe Funk-Radon transform [13]. Note that with these examples,we do not intend to provide a quantitative comparison betweenQBI and CSD, but rather demonstrate that our multi-fibervisualizations can be applied to different diffusion approaches.As such, standard QBI and CSD parameters were used asreported previously: Tuch [13] and Descoteaux et al. [38] forQBI; and Tournier et al. [14] and Jeurissen et al. [20] for CSD.Noteworthy is that, in contrast to the fODF (e.g., see 39,40),the dODF calculated with QBI is a spherical probabilitydistribution, and thus normalized to unit probability over thesphere. To account for this difference, we have used twoscaling approaches that yield comparable ODFs, both in theirglyph representation and in their basis to form thehyperstreamline. For the dODF, standard “min-max” scalingwas used, as proposed by Tuch [13]. For the fODF scaling, wehave used a similar scaling, here called “normalization scaling”,where the amplitudes of the fODF in each voxel are scaledsuch that the maximum amplitude is equal to one. Deterministicfiber tractography was performed using the peak fiber

Figure 3. Difference between hyperstreamlines and streamribbons. A single tract-of-interest from a simulated fiberconfiguration (a) is created as hyperstreamline (b-e) and streamribbon (c,f). In b), the fODF at a location along this tract (white tube);c) fODF shown semi-transparently with its peak orientations; d) fODF shown with the plane perpendicular to the tract orientation,delineating the amplitude of the hyperstreamline; e) the hyperstreamline; f) streamribbons are created of the fODF peaks that do notcorrespond to the tract orientation.doi: 10.1371/journal.pone.0081453.g003



orientations of the ODFs, where the number of unique fiberpopulations at each location, and their orientations, werecomputed as described in Jeurissen et al. [23]. ODF peakthresholds were defined as 10% of their maximum value. Themaximum number of unique fiber populations was limited tothree for all analyses. Fiber tractography using both methodswas performed with the ExploreDTI diffusion MRI toolbox [41](www.exploreDTI.com).

Multi-fiber tractography visualizationThe conventional representations of fiber pathways are

either streamlines (e.g., Basser et al. [3]) or streamtubes [4,42].Hyperstreamline and streamribbon approaches were originallydesigned with the purpose of visualizing the second and thirdeigenvectors and eigenvalues of the diffusion tensor [4,6]. Withthe tensor unable to characterize crossing fibers, the tensor-based hyperstreamlines cannot correctly visualize the localarchitecture. In the following sections, we will present the newmulti-fiber tractography visualizations.

Multi-fiber hyperstreamlines. For DTI-basedhyperstreamlines, the cross-sectional shape of thehyperstreamline at each tract position is determined by theorientation of the second and third eigenvectors (scaled as afunction of the eigenvalues) of the diffusion tensor [4]. In thefollowing, we extend this concept for diffusion MRI data with ahigher angular resolution, where the cross-sectional shape isdefined by the ODF, instead of the tensor. For the “multi-fiberhyperstreamline”, the local shape of the hyperstreamlines isthen determined by the three-dimensional ODF profile. At eachtract position, r, we define a circle with its center in r and lyingin the plane perpendicular to the tract orientation, t. Thevectors from r to the points on this circle are then scaled by theODF amplitude along these orientations to delineate the cross-section of the hyperstreamline . For a more detaileddescription, please refer to the pseudo-code in Appendix S1.An example hyperstreamline of the simulated fiber phantom ofFigure 3a is shown in Figure 3b-e. Notice that, by visualizingthe ODF amplitude perpendicular to the tract orientation, themaximum ODF amplitude crossing the tract is not displayed ifpopulations cross at other angles than 90°.

Appendix S3 describes the computational costs of thesehyperstreamlines in more detail.

Multi-fiber streamribbons. Tract ribbons have initially beenproposed to visualize the axial asymmetry of the diffusiontensor [6]. In this work, we introduce “multi-fiber streamribbons”by reducing the ODFs along the tract to their principal peakorientations. In this way, streamribbons can be used forefficient visualization with a lower rendering complexity thanstreamtubes or hyperstreamlines [6,24]. For each ODF peakorientation that does not correspond with the tract orientation, astreamribbon is created – as shown in Figures 2f and 3c,f –which means that in the case of three unique peaks, twostreamribbons are created. For each existing ribbon, theangular deviation is calculated from the current ribbonorientation to the ODF peak or peaks at the next vertex alongthe tract. The ribbon is then connected to the peak thatdeviates the least. In those voxels where the ODF indicates asingle fiber population, the streamribbons converge naturally to

a streamline (Figure 2f). Appendix S2 presents pseudo-codeon how the streamribbons are created.

Appendix S3 describes the computational costs of thesehyperstreamlines in more detail.

Color-encoding. The conventional coloring of streamlinesand -tubes shows the tract orientation at each vertex, providingadditional visual cues about the tract orientation such as the“direction encoded color” (DEC) map proposed by Pajevic andPierpaoli [43]. This coloring according to the diffusionorientation can still be used for our proposed visualizations,further enhancing the interpretation of the local microstructuralorganization. To this end, we propose such color-encodingscheme, termed ‘ODF color-encoding’, where:

• All tract vertices with a single fiber population are coloredaccording to the tract direction;

• Vertices with two unique fiber populations, where onepopulation corresponds to the tract direction, are coloredaccording to the orientation of the population crossing the tract;

• Vertices with three or more populations have the individualpoints on the hyperstreamline circumference colored by theorientation of that point with respect to the tract vertex.

As an alternative to the proposed ODF color-encoding,where the orientations of the fiber populations are highlighted,it is also possible to highlight the number of fiber populations.This can be used to distinguish between regions with one, two,or more than two fiber populations more clearly (as also shownin Jeurissen et al. [23]).

In vivo tract visualizationsIn vivo examples of multi-fiber tractography visualization are

shown for fiber tracts from the lateral projections of the corpuscallosum (abbreviated as latCC), the corticospinal tract (CST),and the arcuate fasciculus (AF), all of which are known tointersect other WM structures [44]. In addition, tracts from thebilateral cingulum bundles are shown, as an example of fiberbundles with a relatively small cross-sectional area. Tomaintain the focus on the additional information conveyed byour new visualization approaches, these examples are onlyshown for the CSD results. For a specific configuration of AFpathways, however, we provide an example illustrating thatboth QBI and CSD based tractography results can benefit frommulti fiber visualizations.

Results

SimulationsFigure 2a shows an example fiber configuration, where there

are regions with single fiber populations as well as regions withtwo and three fiber populations crossing, as can also be seenfrom the fODF glyphs (calculated from CSD) shown per voxelin Figure 2b. The tensor-based hyperstreamline andstreamribbon are shown in Figures 2c and 2d, respectively.Creation of the hyperstreamline is shown in Figure 2e. Whendisplayed at each vertex of the fiber tract, the fODF glyphs inFigure 2e illustrate the local microstructure, with one or twopopulations crossing the fiber tract, depending on the locationalong the tract – as can be verified from Figures 2a and 2b.



http://www.exploredti.com

The step-by-step creation of the correspondinghyperstreamline is also shown in Figure 2e, where the ODFcolor-encoding further highlights the architectural organization.The multi-fiber streamribbon is created by continuouslyconnecting the peak orientations and magnitudes of thepopulations crossing the fiber tract. In Figure 2f, the peakorientations are shown along the tract as cylinders with thestreamribbons connecting these peaks and for two differentcolor-encodings proposed in this work. Notice that the tensor-based visualizations (Figures 2c and 2d) show some contrastalong the tract between regions with one, two, and three fiberpopulations, but they do not visualize the orientations of theunderlying fiber populations in an unambiguous way. The multi-fiber based visualizations, on the other hand, do show the fiberorientations very clearly, both as hyperstreamline and asstreamribbons.

The simulated fiber phantom in Figure 2 has three fiberpopulations that are oriented perpendicularly. Thus, the peakorientations were perpendicular to the tract direction, where thehyperstreamline envelops the full ODF profile (Figure 2e).However, if populations are no longer orthogonal, the ODFprofile perpendicular to the tract no longer describes the peakamplitude of the ODF. As a result, the hyperstreamline andstreamribbons show different complementary characteristics ofthe fiber populations (as can be seen when comparing Figure3e and 3f).

In Vivo Tract VisualizationsIn the following subsections, in vivo examples of fiber

bundles that pass through regions of complex fiber architectureare shown, demonstrating the additional information visualizedwith these new multi-fiber tractography representations.

Corpus callosum. Fiber tracts from the lateral projectionsof the corpus callosum (latCC) are displayed in Figure 4.Hyperstreamlines are shown for subject one in an axialorientation (a) and for subject two in a coronal orientation (b);with the tract segment in the boxed regions enlarged in c) andd), respectively. Figure 4c,d also show that the ODFamplitudes perpendicular to the fiber tract pathway provide thecross-sectional shape of the multi-fiber hyperstreamline. VideoS1 shows this creation process in more detail. When starting atthe mid-sagittal region, the tract pathway first crosses the CSTand then the AF, both clearly depicted in the ODF glyphs andthe hyperstreamlines as the (blue/purple) inferior-superior and(green) anterior-posterior fiber populations, respectively. Ascan most clearly be observed in the hyperstreamline that iscolored by the number of ODF peaks – indicated by the redarrow in d) – there are regions along this tract with three fiberpopulations. In c) and d), these tract segments can also beobserved as the multi-fiber streamribbons.

Cortico-spinal tracts. Fiber tracts from the CST are shownin Figure 5. Global overviews of the mid-sagittal slice of thebrain with the hyperstreamline are shown in a) for subject oneand e) for subject two. Figure 5b,c shows how a small segmentof the tract in the region of the pons – see yellow rectangle ina) – is visualized as a multi-fiber hyperstreamline. In d), thecorresponding streamribbon is illustrated. For subject two, thehyperstreamline and streamribbon are shown in e-h).

According to the known anatomy in this region, there are clearindications for left-right oriented transverse pontine fiberpopulations (also seen in Tournier et al. [10] and Aggarwal etal. [45]) and front-back oriented fiber populations of the middlecerebellar peduncle [46]. More superiorly along the CST onecan also clearly observe anterior-posterior oriented fiberpopulations crossing the tract, indicated by the red arrows in a)and e).

Arcuate fasciculus. Figure 6 shows a multi-fibervisualization of the left arcuate fasciculus (AF). Thehyperstreamline and streamribbon representations bothillustrate the orientations of the fiber populations crossing theAF in accordance with the known local architecture.Enlargements of the indicated region (yellow rectangle in a))are shown sagittally (b,c) and axially (d,e), clearly indicatingthat there are two other fiber populations (latCC in reddish andCST in bluish) crossing the AF in this region. An oblique viewof the same tract segment is presented in f), showing theamplitudes of the fiber populations of the latCC and CST andtheir continuity along the tract pathway in more detail. Thereare also anterior-posterior oriented fiber populationsintersecting the AF at its more posterior part, correspondingwith the inferior fronto-occipital fasciculus [46] (Figure S1).Video S2 shows this hyperstreamline in full detail.

To demonstrate that multi-fiber tractography visualizationscan depict the microstructural architecture not only for a singletract pathway but also for whole fiber bundles, Figure 7 showsa comparison of the left AF between standard streamtubes (a),multi-fiber hyperstreamlines (b), and streamribbons (c) withorientation color-encoding. In d), the conventional streamtuberepresentation is used, but with the orientation color-encodingfrom the ODF as shown in b).

When generating tractography data with different methods,subtle differences between them can be observed using theproposed visualization approaches (as illustrated in Figure 8).A part of the right AF is shown with QBI-based tractography (a)and CSD-based tractography (b) with the conventional tractrepresentation. For each approach, a single pathway is shownas a QBI hyperstreamline (c) and a CSD hyperstreamline (d),highlighting the subtle differences in ODF reconstructionbetween QBI and CSD in the superior portion of the AF asindicated with the red arrow. In e) and f), the AF pathways(green) are shown in combination with the post-hocreconstructed latCC trajectories (red) in the region of the redarrow, confirming the intersection of (part of) the latCCpathways.

Cingulum. For the bilateral cingulum bundles (Figure 9a),one tract pathway has been selected towards the bottom of thecingulum, i.e., an “edge” tract located more towards theinterface with the corpus callosum (red in Figure 9b), and onetract pathway that is located more at the “center” of the bundles(green in Figure 9b). These “center” and “edge” tracts areshown in Figures 9c,d and 9e,f respectively, from a frontal-superior angle with the same hyperstreamline settings. Astrong difference in the width of the hyperstreamlines can beobserved between the center (d) and edge (f) tracts, reflectinga marked difference in fiber architecture in these differentregions of the cingulum. Notice that even the “center” tract



Figure 4. Hyperstreamlines and streamribbons for a tract from the corpus callosum. Axial (a) and coronal (b) slices of thebrain of the two subjects (subject one: a) and c); subject two: b) and d)) are shown, with a tract from the lateral projections of thecorpus callosum (latCC) visualized as multi-fiber hyperstreamline. The boxed regions in a) and b) are enlarged in c) and d),respectively, showing the construction procedures of the hyperstreamline and streamribbon. Starting from the middle of the brain,the fiber tracts first cross the cortico-spinal tracts (CST) before intersecting the arcuate fasciculus (AF) more laterally. From thevisualizations in c) and d), regions with three distinct fiber populations can be seen along the tracts, i.e., where the AF and CST bothcross the latCC pathway. This is highlighted when color-encoding the hyperstreamline by the number of ODF peaks (red arrow).doi: 10.1371/journal.pone.0081453.g004



shows left-right oriented populations along most of itstrajectory.

Discussion

In this work, we have developed multi-fiber tractographyvisualization strategies that combine information of local white

Figure 5. Hyperstreamlines and streamribbons for a tract from the cortico-spinal tract. A global overview of the mid-sagittalslice of the brain with hyperstreamline is shown in a) for one subject. A segment of the cortico-spinal tract (CST) in the region of thepons – indicated on a) by the yellow rectangle – is enlarged in b-d). The multi-fiber hyperstreamline is shown in b) and c), indicatingleft-right (LR, red) and anterior-posterior (AP, green) oriented fiber populations. This can also be seen from the streamribbonrepresentation in d). The white ellipses (b-d) highlight a region where the LR-oriented fibers are not perpendicular to the tractpathway, resulting in a hyperstreamline that does not reflect the full ODF amplitude, whereas the streamribbons do. For the secondsubject, f-h) show the multi-fiber hyperstreamline and streamribbon representations of a small segment of the tract pathwayindicated by the yellow rectangle on e). Note that more superior along the CST one can detect prominent AP-oriented fiberpopulations that correspond to the arcuate fasciculus (red arrows in a and e).doi: 10.1371/journal.pone.0081453.g005



matter fiber architecture – e.g., the information captured by thedODF or fODF – with global anatomical information from fibertractography, so as to create more complete representations ofthe microstructural organization of the WM. Thesevisualizations will be made freely available to the community,as part of the ExploreDTI diffusion MRI toolbox [41](www.exploredti.com).

The two proposed approaches, multi-fiber hyperstreamlinesand multi-fiber streamribbons, visualize different properties ofthe ODFs, with the most pronounced difference in situationswhere fiber populations are not orthogonal (as illustrated inFigure 3). In vivo, when fiber population orientations willgenerally not be orthogonal, the two methods can be used tovisualize complementary information from the ODF. An

Figure 6. Hyperstreamlines and streamribbons for a tract from the arcuate fasciculus. a) An example of the multi-fiberhyperstreamline and streamribbon is shown for a single tract of the arcuate fasciculus (AF). Tract segment indicated by the yellowrectangle in a) is shown in a sagittal (b,c) and axial (d,e) view, for both the hyperstreamline (b,d) and streamribbon (c,e). The samesegment is shown in f) from a near coronal view angle, indicating (from left to right): the ODF glyphs along the tract; thecorresponding multi-fiber hyperstreamline; the glyph objects representing the ODF peak orientations and magnitudes; and thecorresponding multi-fiber streamribbon. The inset depicts the oblique viewing angle. Right-left and inferior-superior oriented fiberpopulations are visible crossing the AF and represent the lateral projections of the corpus callosum and the cortico-spinal tracts,respectively.doi: 10.1371/journal.pone.0081453.g006



http://www.exploredti.com

example of this can be observed in the pons, highlighted by thewhite ellipse in Figure 5b-d. From the streamribbon (d), it isclear that the magnitudes of the fiber populations in the shownsegment do not differ much. This can be verified from the ODFglyphs visualized along the tract (b), but this is not apparent inthe hyperstreamline (c). In the superior part of the AF (Figure6d,e), a similar difference in visualization of ODF propertiescan be seen between the hyperstreamline and thestreamribbon. In general, for interpretation of the ODF peakmagnitudes, the streamribbons are preferable. However, due to

the two-dimensional nature of a ribbon, investigating thespecific configuration of the streamribbons can be non-trivial.By reducing of the full ODF to their peak orientations, theinformation about the shape of the peaks is discarded, makingit impossible to distinguish between sharp or very broad ODFpeaks. The three-dimensional nature of the hyperstreamlineslends itself to more intuitive interpretations of the localarchitecture. In some situations, for instance in the absence offree water diffusion, the fODF is modeled as a very spikyfunction (e.g., 47,48). In such cases, where fODF lobes

Figure 7. Arcuate fasciculus visualized as streamtubes with different color-encoding. In a), the arcuate fasciculus (AF) isshown with its conventional streamtube representation and with color-encoding according to the tract direction. The multi-fiberhyperstreamline and streamribbon with the orientation color-encoding according to the ODF are shown in b) and c), respectively.Standard streamtubes have been visualized in d), but then using the ODF-based color-encoding used in b).doi: 10.1371/journal.pone.0081453.g007



resemble delta-peaks, the hyperstreamlines essentially“collapse” to streamribbons.

By comparing multi-fiber hyperstreamlines of fiber tractsreconstructed with two different approaches to estimate theODF, we have demonstrated that this method can be used toshow subtle differences between the results of the two

methods that with conventional fiber tractography visualizationswould have gone unnoticed. In Figure 8, for instance, the latCCpathways were interdigitating the AF in only one of the diffusionmethods as suggested by the hyperstreamlines. The validity ofthis observation was backed up by finding a difference inconfiguration of the latCC pathways between both approaches.

Figure 8. Example comparison of hyperstreamlines created using two HARDI methods. Hyperstreamline examples tocompare different methods. The reconstructed arcuate fasciculus (AF) is shown for QBI (a) and for CSD (b). Single tracts from theQBI bundle and CSD bundle are shown as a multi-fiber hyperstreamline in c) and d), respectively. This visualization, both in cross-sectional shape as well as color-encoding, highlights an important difference between the two used methods. For CSD (d), clearleft-right fiber populations (red) can be seen crossing the AF (indicated by the arrow), whereas QBI (c) does not display thesepopulations: these lateral projections of the corpus callosum (latCC) could not be detected with QBI. Verification can be seen in e)and f), where the AF is shown in green and the latCC in red (seeded lateral to the AF it should target the corpus callosum, as seenin f).doi: 10.1371/journal.pone.0081453.g008



However, it should be clear that in this work, it was not our aimto contrast different diffusion reconstruction methods in termsof “accuracy” or “validity”, but purely to illustrate that theproposed multi-fiber hyperstreamlines can be an exploratorymeans to investigate these methods more intuitively.

The proposed multi-fiber hyperstreamlines andstreamribbons can be extended to any multi-fiber diffusionmodel. For instance, one could opt to display the ball-and-multiple-stick model [17] using a streamribbon for each of the“stick” compartments when more than one “sticks” are present.Alternatively, the multiple-tensor approach [49] can bevisualized by combining those diffusion ellipsoids that do notbelong to the tract itself as hyperstreamlines or by using theprincipal diffusion directions to construct streamribbons.

When one is presented with a global view of an entire fiberbundle as in Figure 7, distinguishing the shape of the individualhyperstreamlines becomes complicated. The amount ofinformation in these hyperstreamlines and streamribbons couldresult in an image that is too cluttered for easy interpretation.As a more subtle alternative to visualize local architecturalinformation, without making the images too complex to

interpret, the hyperstreamlines can be reduced to simplestreamtubes, while maintaining the ODF color-encoding. Inaddition, streamtubes have a lower computational complexitycompared with the multi-fiber hyperstreamlines, which could beanother motivation to use the conventional streamtube shape.Video S3 shows the CST visualized as streamtubes (with theconventional color-encoding (left) and ODF color-encoding(right). The ODF color-encoded streamtubes show thepresence, location, and orientation of crossing fiber populationsalong the CST, displaying only a single fiber population in theregion of the internal capsule.

The initial hyperstreamline and streamribbon approacheswere designed with the purpose of visualizing the diffusiontensor in more detail [4,6]. Hyperstreamlines have also beenused to convey information on the uncertainty in fiberorientation, where the width of the hyperstreamline representsthe local “cone of uncertainty” of the first eigenvector [9,50].Alternatively, streamsurfaces have been proposed to visualizeregions of planar diffusion as surface structures [4]. Forinstance, at interfaces between fiber bundles where partialvolume effects cause the diffusion profile to be more planar in

Figure 9. Hyperstreamlines and streamribbons for a tract from the cingulum. Superior segment of the bilateral cingulumbundles (a). From these full bundles – shown in b) as a yellow haze for anatomical reference – one tract has been selected at thecenter of each bundle (shown in green in b) and one tract at the interface of the corpus callosum (red in b). These “center” (c and d)and “edge” (e and f) tracts have been with the fODF glyphs along their trajectories (c and e) and as hyperstreamlines (d & f). Strongdifference between the magnitudes of the left-right populations can be observed between (c) - (d) and (e) - (f). From the ODFs in c)it is difficult to interpret the continuity of orientation and magnitude of the left-right populations; whereas this is very easy from thehyperstreamlines in (d).doi: 10.1371/journal.pone.0081453.g009



shape, these streamsurfaces create a virtual delineation of theedges of these fiber bundles, aiding in the distinction betweendifferent fiber structures. However, measures of planardiffusion, as used in these streamsurfaces and in conventionalstreamribbons, are not specific for the underlying tissuemicrostructure and are heavily affected by the presence ofcrossing fiber architecture [12]. By contrast, the proposed multi-fiber hyperstreamlines and streamribbons give more specificrepresentations of the microstructural information obtainedfrom diffusion MRI data.

Previous work on visualization of multi-fiber diffusion datahas mainly focused on efficiently displaying the ODF glyphs notonly locally but in larger regions of the brain. Interpretation ofODF profiles of each voxel in an entire imaging slice canbecome difficult by the immense amount of data visualized.Reducing the ODF to its peak orientations yields more easilyinterpretable data in such situations, with the additional benefitof being less memory-consuming and more rendering-efficient[24]. With the development of advanced interactive andexploratory tools for visualizing ODF glyphs, however, it hasbecome possible to visualize the full ODFs efficiently in largequantities, e.g., for an entire slice [26,51]. Recent work hasfocused on representing the ODF glyphs at discrete pointsalong a tract [25,27], whereas the multi-fiber hyperstreamlinesproposed in this work provide a continuous and, hence, a moreintuitive representation of the data. To further emphasize thisdifference, an example of the discrete and continuous way tovisualize a fiber trajectory is given in Figure 10 using both DTI-

based and multi-fiber reconstructions. Plotting the firsteigenvectors yields the discrete version of a reconstructedtract, but the tract itself gives a continuous and, therefore, moreintuitive representation of the data. This is also the case for themulti-fiber hyperstreamline, which – being also continuous –gives a more complete view compared to showing ODF glyphsonly at discrete locations along the tract pathway. Thisobservation is supported by the in vivo examples shown inFigures 4c,d, 6f, and 9, where data interpretation for onecontinuous 3D object, the hyperstreamline, is morestraightforward than for the individual 3D objects, which canobscure each other. Furthermore, as can be seen in Figures4a,b, 5a,e, hyperstreamlines can directly pinpoint the mainareas of crossing fibers, where individual glyphs are lesspowerful. This observation can also be made in Figure 2b ofKezele et al. [25].

When trying to visualize the fiber architecture along aspecific fiber tract, alternatives to the multi-fiber visualizationmethod proposed here are possible. Conceptually, it might bevery helpful to show which fiber pathways cross a specific tract-of-interest, as this shows information on the fiber organizationat this tract-of-interest. However, showing theseperpendicularly crossing pathways can clutter the image,obscuring the view of the tract-of-interest, as shown in Figure11a. The proposed methods provide a more succinctrepresentation of the local tissue architecture, as shown inFigure 11b for the multi-fiber hyperstreamline. This is shown in

Figure 10. The difference between discrete and continuous visualization. A coronal overview of the tract to be visualized isseen in a), with the main eigenvector at discrete locations along the tract (b) and the tract itself (c). Analogous to b) and c), d) and e)show the fODF glyphs at discrete locations along the tract and the multi-fiber hyperstreamline, respectively. The continuity is difficultto grasp from the glyphs alone (b and d), whereas the continuous representations (c and e) give a more intuitive feel, are easier tointerpret, and represent a more complete picture of the underlying WM pathway.doi: 10.1371/journal.pone.0081453.g010



a more detail in in Video S4 (for a single tract from the AF for adifferent subject).

An important and promising clinical application of fibertractography is surgical planning. Since the initial case reportsin the literature (e.g., Coenen et al. [52]), its use in surgicalplanning is steadily growing. A recent overview on the use oftractography has foretold a promising future, stating that it “willbecome established as a routine clinical investigation in manycenters in the coming years” [53]. In this prospect, Ciccarelli etal. [53] believe that improvements in tractography visualizationsare of paramount importance to fully benefit from tractographyinformation. With several studies already demonstrating thatpost-surgical outcome is improved if fiber tracking is used inpre-operative planning [30,54], and predicting, to some degree,the clinical improvements after treatment [55,56], anyimprovements in visualization of fiber tracts and local tissuemicrostructure can only be considered beneficial for surgicaloutcome.

Recent research shows that the vast majority of WM voxelscontains more than one fiber population with approximately 25to 50% containing more than two fiber populations, dependingon the specific diffusion model [23]. This makes the use ofODF-based methods less of a luxury and more a necessity,both in biomedical research and clinical applications (e.g.,31,57-60). More specifically, ODF-based multi-fibertractography is beginning to show improved clinical results overtensor-based tracking, in the presence of tumors [56] and insurgical target localization for deep brain stimulation [57], which

further stresses the need for multi-fiber visualizationapproaches.

In conclusion, we have shown that multi-fiber tractographyvisualizations can display the local fiber architecture along fibertrajectories, combining the detailed tissue characterizationcaptured in the ODF with the global anatomical informationfrom multi-fiber tractography. These new visualizationapproaches create a more complete picture of the WMmicrostructure for tracts that traverse through areas of complexfiber configurations. By facilitating the interpretation oftractography data, these multi-fiber hyperstreamlines andstreamribbons may improve our understanding of white mattercharacteristics.

Supporting Information

Figure S1. Arcuate fasciculus crossing the inferior fronto-occipital fibers. In a), the inferior fronto-occipital fasciculus(IFOF) is shown crossing a posterior part of the arcuatefasciculus (AF). Enlarging the region where these pathwayscross (b) clearly illustrates that the hyperstreamline visualizesthis anterior-posterior fiber population. For detailedinterpretation, the hyperstreamline is shown in c) without theIFOF. In d), the hyperstreamline is colored by the number ofunique fiber populations – where red indicates 1, green is 2,and blue more than 2 fiber populations.(TIF)

Figure 11. Visualization of local tract orientations crossing a fiber tract. A single tract from the arcuate fasciculus (AF), thesame as in Figures 5 and 6. a) Tract shown as a thick streamtube with fibers crossing this tract of interest shown as thinnerstreamtubes. b) Tract shown as multi-fiber hyperstreamline.doi: 10.1371/journal.pone.0081453.g011



Figure S2. Conceptual illustration of the creation of ahyperstreamline. For a point r along the tract, a number ofpoints is defined in a circle around r perpendicular to the tractorientation t (a), and vectors from r to these points arecalculated (b). These vectors are then scaled according to theODF amplitude along these vectors (c), delineating the cross-sectional shape of the hyperstreamline at point r.(TIF)

Video S1. Creation of a hyperstreamline for a tract fromthe lateral projections of the corpus callosum.(MPG)

Video S2. Creation of a multi-fiber hyperstreamline for afiber tract from the arcuate fasciculus.(MPG)

Video S3. The cortico-spinal tracts visualized asstreamtubes with different color-encoding. On the left, theconventional color-encoding was used; the ODF color-encoding was used on the right. The ODF color-encodedstreamtubes show the presence, location, and orientation ofcrossing fiber populations along the CST, displaying only asingle fiber population in the region of the internal capsule.(MPG)

Video S4. Visualization of local tract orientations crossinga fiber tract. Visualization of all fiber tracts crossing such afiber pathway can be informative to show the large-scale

connectivity, but obscures the pathway of interest. By insteadvisualizing the local microstructure captured in the ODF, itbecomes possible to visualize the complex tissue architecturelocally along a fiber tract in a compact and elegant manner.(MPG)

Appendix S1. Pseudo-code for generating multi-fiberhyperstreamlines.(DOCX)

Appendix S2. Pseudo-code for generating multi-fiberstreamribbons.(DOCX)

Appendix S3. Background on computational cost ofvisualizations.(DOCX)

Acknowledgements

The authors would like to thank Fredy Visser for acquiring theMR data.

Author Contributions

Conceived and designed the experiments: SBV MAV AL.Performed the experiments: SBV. Analyzed the data: SBV.Contributed reagents/materials/analysis tools: SBV AL. Wrotethe manuscript: SBV MAV AL.

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